Representability of the Direct Sum of q-Matroids

11/21/2022

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by   Heide Gluesing-Luerssen, et al.

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q-Matroids are the q-analogue of matroids. In this short note we consider the direct sum of q-matroids, as introduced recently in the literature. We show that the direct sum of representable q-matroids may not be representable. It remains an open question whether representability of the direct sum can be characterized by the given q-matroids.